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Nonoscillatory half-linear difference equations and recessive solutions

Abstract

Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the "smallest solutions in a neighborhood of infinity," like in the linear case. Other asymptotic properties of recessive and dominant solutions are treated too.

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Correspondence to Mariella Cecchi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cecchi, M., Došlá, Z. & Marini, M. Nonoscillatory half-linear difference equations and recessive solutions. Adv Differ Equ 2005, 676580 (2005). https://doi.org/10.1155/ADE.2005.193

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